SECTION B
MARKS: 150
This memorandum consists of 25 pages.
QUESTION 1
|1.1 |Mean = [pic] |( 522,5 |
| | |( answer |
| |ANSWER ONLY: Full marks |(2) |
| | |No penalty for |
| | |Rounding: |
| | |Accept 43,54 ; 44 |
|1.2 |Ordered Data |( 9,3 |
| |9,3 14,9 15 23,6 26,1 28 32,5 60,9 65,7 71,9 76,4 98,2 | |
| | |( 19,3 |
| |Median = [pic] = 30,3 |( 30,3 |
| |Lower quartile = [pic] =19,3 |( 68,8 |
| |Upper quartile = [pic] = 68,8 | |
| | |( 98,2 |
| |The five number summary is (9,3 ; 19,3 ; 30,25 ; 68,8 ; 98,2) |(5) |
| |OR | |
| |If they use the formula: |If indicated on the box and |
| |Ordered Data |whisker diagram in 1.3 – |
| |9,3 14,9 15 23,6 26,1 28 32,5 60,9 65,7 71,9 76,4 98,2 |5 marks |
| |Position of median: [pic] | |
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| |Position of lower quartile: [pic] | |
| |[pic] | |
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| |Position of upper quartile: [pic] | |
| |[pic] | |
| |Min = 9,3 | |
| |Max = 98,2 | |
| | | |
| |Accept any one of these five number summaries: | |
| |(9,3 ; 19,3 ; 30,3 ; 68,8 ; 98,2) | |
| |(9,3 ; 15 ; 30,3 ; 71,9 ; 98,2) | |
| |(9,3 ; 17,2 ; 30,3 ; 70,4 ; 98,2) | |
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|1.3 | | |
| | |( minimum and maximum values |
| | |( quartiles and median |
| | |( whiskers with |
| | |median line |
| | |(3) |
|1.4 |The data is skewed to the right (positively skewed). |( ( comment about |
| |This suggests that there was a large difference between the median and the maximum rainfall (some |rainfall. |
| |months had exceptionally high rainfall in that year). |(2) |
| | |Note: |
| |Die data is skeef na regs (positief skeef) |Skewed to right 1/2 |
| |Dit dui daarop dat daar ’n groot verskil is tussen die mediaan en die maksimum reënval (sommige | |
| |maande het ongewoon hoë reënval gehad gedurende die jaar. | |
| | |( ( verwysing na |
| | |reënval |
| | |(2) |
|1.5 | By using the calculator, [pic]. (28,19058256) |(((answer |
| | |Accept: 28 ; 28,2 ; 28,1 |
| |OR Pen and Paper method (not recommended) |(3) |
| |Mean = 43,54 (43,54166667) | |
| |x | |
| |[pic] | |
| |[pic] | |
| | | |
| |60,9 | |
| |17,36 | |
| |301,3696 | |
| | | |
| |14,9 |(headings correct |
| |-28,64 |(sum of the squares of the mean |
| |820,2496 |deviations |
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| |9,3 | |
| |-34,24 | |
| |1172,378 |( answer |
| | |(3) |
| |28,0 |[15] |
| |-15,54 | |
| |241,4916 | |
| | | |
| |71,9 | |
| |28,36 | |
| |804,2896 | |
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| |76,4 | |
| |32,86 | |
| |1079,78 | |
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| |98,2 | |
| |54,66 | |
| |2987,716 | |
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| |65,7 | |
| |22,16 | |
| |491,0656 | |
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| |26,1 | |
| |-17,44 | |
| |304,1536 | |
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| |32,5 | |
| |-11,04 | |
| |121,8816 | |
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| |23,6 | |
| |-19,94 | |
| |397,6036 | |
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| |15,0 | |
| |-28,54 | |
| |814,5316 | |
| | | |
| |Sum | |
| |9536,509 | |
| | | |
| |[pic] (28,19059…..) | |
QUESTION 2
|2.1 |Linear or Exponential |( answer |
| | |(1) |
|2.2 | | |
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| | |( (line of best fit |
| | |(2) |
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| |For this set of data we will accept the straight line. | |
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|2.3 |The scatter plot shows an overall decrease in the time taken by the winner since 1972. |( decrease/afname |
| |Die spreidiagram dui ‘n algehele afname in tye aangeteken deur die wenners vanaf 1972. |(1) |
| |OR | |
| |Times are faster. Tye is vinniger. | |
| |OR | |
| |Negative correlation between year and time. | |
| |Negatiewe korrelasie tussen jaar en tyd. | |
|2.4 |The top athletes of the world have turned professional. This allows them to train at the best | |
| |facilities and receive the best coaching available. |( any acceptable reason relating |
| |Also, equipment manufacturers are in competition with each other. In this case, manufacturers are |to the trend |
| |designing swimsuits that assist swimmers |(1) |
| |Swimmers train harder and put in more effort. | |
| |Die top atlete van die wêreld het professionele atlete geword. Dit laat hulle toe om by die beste| |
| |fasiliteite te oefen en die beste afrigting te ontvang. |( enige aanvaarbare rede wat |
| |Vervaardigers van voorraad is in kompetisie met mekaar. Hul onwerp dus swembroeke wat die |verband hou met die neiging. |
| |swemmers help. |(1) |
| |Swemmers oefen harder en gebruik meer tyd om te oefen. | |
|2.5 |In the context of the times around these two observations, one can consider the efforts of 1976 |((acceptable reason |
| |and 1988 to be outliers. This shows that these athletes were exceptionally good swimmers at the |in context |
| |time. |(2) |
| |Binne die konteks van tye gedurende hierdie twee waarnemings, kan die poging van 1976 and 1988 |((aanvaarbare rede binne die |
| |gesien word as uitskieters. Dit dui daarop dat hierdie atlete uitstekende swemmers was daardie |konteks |
| |tyd. | |
| | |(2) |
|2.6 |Winning time of 2008 is expected to be about 47,6 seconds. |(answer from graph |
| |Accept answer from candidate’s graph. |(1) |
| | |[8] |
QUESTION 3
|3.1 |50 |( answer |
| | |(1) |
|3.2 |Cut–off mark of 56% (37 students)or 58% (38 students) |( answer read off from ogive |
| |Accept interval: 55% - 60% |(1) |
|3.3 |Marks | |
| |(out of 100) | |
| |Frequency ( f ) | |
| | |( class intervals |
| |0 ( marks ................
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